کد مقاله کد نشریه سال انتشار مقاله انگلیسی ترجمه فارسی نسخه تمام متن
5775736 1631745 2017 10 صفحه PDF سفارش دهید دانلود رایگان
عنوان انگلیسی مقاله ISI
Two-walks degree assortativity in graphs and networks
ترجمه فارسی عنوان
دو طرفه در سطح گراف ها و شبکه ها قرار می گیرند
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کلمات کلیدی
نمودارها، شبکه های دنیای واقعی پیاده روی، جذابیت،
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات ریاضیات کاربردی
چکیده انگلیسی
Degree assortativity is the tendency for nodes of high degree (resp. low degree) in a graph to be connected to high degree nodes (resp. to low degree ones). It is usually quantified by the Pearson correlation coefficient of the degree-degree correlation. Here we extend this concept to account for the effect of second neighbours to a given node in a graph. That is, we consider the two-walks degree of a node as the sum of all the degrees of its adjacent nodes. The two-walks degree assortativity of a graph is then the Pearson correlation coefficient of the two-walks degree-degree correlation. We found here analytical expression for this two-walks degree assortativity index as a function of contributing subgraphs. We then study all the 261,000 connected graphs with 9 nodes and observe the existence of assortative-assortative and disassortative-disassortative graphs according to degree and two-walks degree, respectively. More surprisingly, we observe a class of graphs which are degree disassortative and two-walks degree assortative. We explain the existence of some of these graphs due to the presence of certain topological features, such as a node of low-degree connected to high-degree ones. More importantly, we study a series of 49 real-world networks, where we observe the existence of the disassortative-assortative class in several of them. In particular, all biological networks studied here were in this class. We also conclude that no graphs/networks are possible with assortative-disassortative structure.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Applied Mathematics and Computation - Volume 311, 15 October 2017, Pages 262-271
نویسندگان
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